SOLUTION: I am lost on this one???????? Find a polynomial of degree 12 with zeroes and 5,-3/8 and 4+5i thanks

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Question 58859: I am lost on this one????????

Find a polynomial of degree 12 with zeroes and 5,-3/8 and 4+5i

thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find a polynomial of degree 12 with zeroes and 5,-3/8 and 4+5i
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If 4+5i is a zero, 4-5i is a zero.
Let 5 be of multiplicity 5
Let -3/8 be of multiplicity 5
Then:
f(x)=(x-5)^5 (8x+3)^5 (x-4-5i)(x-4+5i)
is a polynomial of degree 12 with
the required zeroes.
Cheers.
Stan H.